I don't think I have ever seen a Midori Apple Martini, but I will ask around.

Midori is a melon liqour, so I'm not sure if it would make a very good apple martini. Most of the Apple Martini's I have seen have been made with Apple Pucker. Perhaps the green color has thrown you into thinking it has Midori in it?

Anyhow... a VERY BASIC apple martini:

1 part Vodka - an apple infused vodka is a great choice, but you can use an unflavored one. If you use an unflavored vodka the next ingredient is 1 part apple pucker, if you use a flavored vodka go with 1/2 part Pucker.

From here on out it is a free for all, some people throw in 1 part apple juice, others use white grape juice (really quite good), still others throw in a spash of crown royal, a slpash of 7 up and a spash of sweet an sour (yech).

I hope I was of some help, I'll be gald to give you more info if you like!